The Power Spectrum, Bias Evolution, and the Spatial Three-Point Correlation Function

We calculate perturbatively the normalized spatial skewness, S3, and full three-point correlation function (3PCF), ζ , induced by gravitational instability of Gaussian primordial fluctuations for a biased tracer-mass distribution in flat and open cold-dark-matter (CDM) models. We take into account the explicit dependence on cosmological parameters, the shape and evolution of the CDM power spectrum, and allow the bias to be nonlinear and/or evolving in time, using an extension of Fry’s (1996) bias-evolution model. We derive a scale-dependent, leading-order correction to the standard perturbative expression for S3 (Fry & Gaztañaga 1993) in the case of nonlinear biasing, as defined for the unsmoothed galaxy and dark-matter fields, and find that this correction becomes large when probing positive effective power-spectrum indices, i.e., scales above 100 h Mpc for reasonable CDM models. This term implies that the inferred nonlinear-bias parameter, as usually defined in terms of the smoothed density fields, might in general depend on the chosen smoothing scale, and could allow better constraints on both the linearand nonlinear-bias parameters on the basis of skewness measurements alone (or at least distinguish between the smoothed and unsmoothed bias pictures), if S3 could be measured over very large scales. In general, we find that the dependence of S3 on the biasing scheme can substantially outweigh that on the adopted cosmology, with linear and nonlinear bias separately giving rise to distinct signatures in [email protected] [email protected]